You will have to file for a waiver of inadmissibility since a prostitution charge is considered a crime involving moral turpitude. In addition, prostitution is an independent ground of inadmissibility if it happened within 10 years of the date to the application for residency. However, it is waivable with a 212h waiver.

I would not travel until taking with an attorney
The prostitution charge will affect your case
I would hire a lawyer

Neil I Fleischer (513) 977-4209 www.immigrate2usa.com
Note: Neil Fleischer is an attorney licensed in the State of Ohio The below answer is provided for informational use only. One should not act or refrain to act solely based on the information provided. No attorney/client relationship is created unless an Agreement is signed by the attorney and the client.
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Neil I Fleischer
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You will not be able to do so without an experienced immigration attorney; at least I would not recommend it. Also, depending on your current status, you may or may not be able to become a resident. First of all, that depends on how you got to the United States and your current status. If you are eligible because you entered legally, etc., then you have to analyze the criminal record. I suggest you contact an experienced immigration attorney. I can offer you a consult here in Houston, if you'd like, to analyze your case.

Avvo doesn't remunerate me for this response, and I'm only offering limited advice based on the few facts given me in your question. I am not your lawyer solely because I answer this question or respond to any follow-up comments. If you want to hire me or are interested in a low cost or free consultation, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. It's impossible to fully evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.